On the distribution of the greatest common divisor of Gaussian integers (Q903132)

We quote the author's perfect abstract: ``For a pair of random Gaussian integers chosen uniformly and independently from the set of Gaussian integers of norm \(x\) or less as \(x\) goes to infinity, we find asymptotics for the average norm of their greatest common divisor, with explicit error terms. We also present results for higher moments along with computational data which support the results for the second, third, fourth, and fifth moments. The analogous question for integers is studied by \textit{P. Diaconis} and \textit{P. Erdős} [in: A Festschrift for Herman Rubin. Beachwood, OH: IMS, Institute of Mathematical Statistics. 56--61 (2004; Zbl 1268.11139)]''.